Problem: Rewrite as a simplified fraction. ${3.\overline{2} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}10x &= 32.2222...\\ 1x &= 3.2222...\end{align*}}$ Subtracting the two equations, we have: ${9x = 29}$ ${x = \dfrac{29}{9}} \text{or} {3 \dfrac{2}{9}}$